A headrest is well-known in the prior art that includes a height-adjustment mechanism. Adjustment of a movable head-support part relative to a fixed support-rod base part is effected for example by an electric motor in this headrest, where gear teeth of the base part and of the movable head-support part mesh with each other. This otherwise advantageous adjustment mechanism needs improvement in terms of its space requirement and the flexibility of the arrangement within the movable head-support part.